scholarly journals Three-loop radiative corrections to Lamb shift and hyperfine splitting

2007 ◽  
Vol 85 (5) ◽  
pp. 509-519 ◽  
Author(s):  
Michael I Eides ◽  
Valery A Shelyuto
Keyword(s):  
Hyperfine Splitting ◽  
Lamb Shift ◽  
Polarization Operator ◽  
Invariant Sets ◽  
Radiative Corrections ◽  
Gauge Invariant ◽  
Electron Polarization ◽  
Electron Line

We consider three-loop radiative corrections to the Lamb shift and hyperfine splitting. Corrections of order α3(Zα)5m are the largest still unknown contributions to the Lamb shift in hydrogen. We calculate radiative corrections to the Lamb shift and hyperfine splitting generated by the diagrams with insertions of one radiative photon and electron polarization loops in the graphs with two external photons. We also obtain corrections generated by the gauge-invariant sets of diagrams with two reducible radiative photon insertions in the electron line and a polarization operator insertion in one of the radiative photons, and diagrams with two reducible radiative photon insertions in the electron line and a polarization operator insertion in one of the external photons. Corrections to the Lamb shift and hyperfine splitting generated by the diagrams with insertions of the three-loop one-particle reducible diagrams with radiative photons in the electron line are calculated in the Yennie gauge.PACS Nos.: 12.20.Ds, 31.30.Jv, 32.10.Fn, 36.10.Dr

Hyperfine splitting in muonium and positronium

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645034 ◽  
Author(s):  
Michael I. Eides ◽  
Valery A. Shelyuto
Keyword(s):  
Hyperfine Splitting ◽  
Invariant Sets ◽  
Gauge Invariant ◽  
Photon Exchange ◽  
Two Photon

Calculation of hard three-loop corrections of order [Formula: see text] to hyperfine splitting in muonium and positronium is reviewed. All these contributions are generated by the graphs with photon, electron and/or muon loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams.

Hard three-loop corrections to hyperfine splitting

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641030
Author(s):  
Michael I. Eides ◽  
Valery A. Shelyuto
Keyword(s):  
Hyperfine Splitting ◽  
Invariant Sets ◽  
Gauge Invariant ◽  
Photon Exchange ◽  
Two Photon

We consider hard three-loop nonlogarithmic corrections of order [Formula: see text] to hyperfine splitting in muonium and positronium. All these contributions are generated by the graphs with photon, electron and/or muon loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams.

First corrections of order α2 (Zα)5 to hyperfine splitting and Lamb shift induced by two-loop insertions in the electron line

1993 ◽  
Vol 312 (3) ◽  
pp. 358-366 ◽  
Author(s):  
Michael I. Eides ◽  
Savely G. Karshenboim ◽  
Valery A. Shelyuto
Keyword(s):  
Hyperfine Splitting ◽  
Lamb Shift ◽  
Electron Line

scholarly journals Three-loop radiative-recoil corrections to hyperfine splitting in muonium

2005 ◽  
Vol 83 (4) ◽  
pp. 363-373 ◽  
Author(s):  
Michael I Eides ◽  
Howard Grotch ◽  
Valery A Shelyuto
Keyword(s):  
Experimental Data ◽  
Hyperfine Splitting ◽  
Theoretical Uncertainty ◽  
Invariant Sets ◽  
Mass Ratio ◽  
Gauge Invariant ◽  
Muon Mass ◽  
Long Time ◽  
Muonium Hyperfine ◽  
Leading Logarithm

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium. These corrections are enhanced by the large logarithm of the electron–muon mass ratio. The leading logarithm-cubed and logarithm-squared contributions were obtained a long time ago. We calculate the single-logarithmic and nonlogarithmic contributions of order α3(m/M)EF generated by gauge invariant sets of diagrams with one- and two-loop polarization insertions in diagrams with two exchanged photons and radiative photons, and by diagrams with one-loop radiative photon insertions both in the electron and muon lines. The results of this paper constitute a next step in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz. They improve the theory of hyperfine splitting, and affect the value of the electron–muon mass ratio extracted from experimental data on the muonium hyperfine splitting.PACS Nos.: 12.20.Ds, 31.30.Jv, 32.10.Fn, 36.10.Dr

Three-loop radiative corrections to the 1s Lamb shift in hydrogen

2019 ◽  
Vol 100 (3) ◽  
Author(s):  
Savely G. Karshenboim ◽  
Valery A. Shelyuto
Keyword(s):  
Lamb Shift ◽  
Radiative Corrections

scholarly journals Gauge and infrared properties of hadronic structure of nucleon in neutron beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

2019 ◽  
Vol 34 (02) ◽  
pp. 1950010 ◽  
Author(s):  
A. N. Ivanov ◽  
R. Höllwieser ◽  
N. I. Troitskaya ◽  
M. Wellenzohn ◽  
Ya. A. Berdnikov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Electron Energy ◽  
Low Energy ◽  
Radiative Corrections ◽  
Quantum Field ◽  
Neutron Lifetime ◽  
Gauge Invariant ◽  
Hadronic Structure ◽  
Lepton Current

Within the standard [Formula: see text] theory of weak interactions, Quantum Electrodynamics (QED) and the linear [Formula: see text]-model [Formula: see text] of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron [Formula: see text]-decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order [Formula: see text], induced by hadronic structure of the nucleon, to the rate of the neutron [Formula: see text]-decay is gauge noninvariant and unrenormalizable. We show that a gauge noninvariant contribution does not depend on the electron energy in agreement with Sirlin’s analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative [Formula: see text]-decay and neutron [Formula: see text]-decay, caused by hadronic structure of the nucleon, are canceled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalizable even formally. Such an unrenormalizability can be explained by the fact that the effective [Formula: see text] vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and [Formula: see text], which are renormalizable theories. We assert that for a consistent gauge invariant and renormalizable analysis of contributions of hadronic structure of the nucleon to the radiative corrections of any order to the neutron decays one has to use a gauge invariant and fully renormalizable quantum field theory including the Standard Electroweak Model (SEM) and the [Formula: see text], where the effective [Formula: see text] vertex of hadron–lepton current–current interactions is caused by the [Formula: see text]-electroweak-boson exchange.

Tests of quantum electrodynamics with EBIT

2008 ◽  
Vol 86 (1) ◽  
pp. 25-31 ◽  
Author(s):  
J Sapirstein ◽  
K T Cheng
Keyword(s):  
Present Status ◽  
Feynman Diagram ◽  
Quantum Electrodynamics ◽  
Nuclear Physics ◽  
Hyperfine Splitting ◽  
Lamb Shift ◽  
Nuclear Recoil ◽  
Correct Treatment ◽  
Charged Ions ◽  
Large Quantum

A Feynman-diagram-based approach to calculating the spectra of highly charged ions is described and applied to lithiumlike and sodiumlike ions. Discrepancies between calculations excluding the two-loop Lamb shift and experiment allow that shift to be determined, as the accuracy of EBIT experiments is well below the size of the effect. The present status of the theory of hyperfine splitting is described, where a large quantum electrodynamics (QED) effect is made difficult to observe because of nuclear physics uncertainties. The importance of a correct treatment of nuclear recoil at present levels of accuracy is stressed, and prospects for a full QED treatment of copperlike ions are discussed. PACS Nos.: 31.30.Jv, 32.30.Rj, 31.25.–v, 31.15.Ar

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